Follow the Leader

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Consider the chart below. The curves are two simple sinusoids, and represent, say, the variance of the height of two swings above the ground as they swing in a simple harmonic motion.

Which of the swings, blue or red, would you say is in the lead?

Which sine curve is in the lead?

For most, the instinct is to believe that the blue swing is in front.

But this would be wrong! The blue swing in fact lagging behind the red swing!

Even with the x axis labelled as “Time”, we are predisposed to visualise the sine curves in space and not in time.

When we read off the sine wave maxima on the x-axis we can see that the blue swing reaches it’s maximum height at t = 1.5 seconds, whereas the red swing already reached it’s maximum height half a second earlier at t = 1 second.

So the red swing is in the lead.

Somehow it seems counter intuitive, that the red swing got there first. It made its history first. It’s sitting there in the past, yet it’s in the lead.

I suppose it depends on how you look at it. Maybe it’s just swings and roundabouts!